Multiply Every Nth Cell By Another Column Whith Merged Cells, THEN Find Column Total

Please see the attached sheet. I have columns B through a lot (B through O in my oversimplified example). In every 7th row in each of these columns there is either a 1 or a blank/zero. I need to multiply that 7th number by the Quantity in column A, to achieve a total (ie the sum of each result of 7th cell*quantity) for each column in the bottom row, labeled "Totals".

In the actual version of my sheet, there are far too many rows to select everything manually. I've been fiddling with combinations of COUNTIF/COUNTA and OFFSET, but I haven't come up with a way to check for the 1 in every 7th row, THEN multiply that 1 by the quantity in column A, THEN add up the results for each column. As you can see, there are 1's elsewhere in the columns that are irrelevant to this particular calculation, so something like LOOKUP would also have to look in every 7th cell and couldn't just look at the column as a whole.

If you can't provide an immediate solution, but can at least point me to a resource that would allow me to devise a way to isolate every 7th row (THAT part is the sticking point), I'll surely post the solution to my own thread with updated keywords if I need it.